What is kurtosis?

Kurtosis tells us how heavy or light the tails of a data distribution are compared to a normal bell shape. It answers whether extreme values happen more often than you would expect in a typical, balanced world.

Imagine you have two groups of students taking a test. Both groups get an average score of 80 points, so their main pile of scores looks the same. But look at the students who did terribly or amazingly well. One group has very few weird scores; most kids are close to the average. The other group has a few kids who scored almost zero and a few who scored perfect, far away from the center. That difference in those distant outliers is what kurtosis measures.

Think of kurtosis like measuring how pointy or flat your data looks when you draw it as a hill.

• A high kurtosis (leptokurtic) means the hill has sharp, steep peaks and very heavy tails. Imagine a mountain with a sharp tip and rocky cliffs far down on either side. In this scenario, most things are clustered tightly in the middle, but extreme events (like stock market crashes or sudden viral hits) happen much more often than usual.
• A low kurtosis (platykurtic) means the hill is flatter with lighter tails. Imagine a gentle rolling hill. The data spreads out more evenly, so you rarely see wild extremes. Most values are just moderately different from the average, not wildly so.

We use kurtosis to understand risk and predictability. If your town’s daily temperatures have high kurtosis, it is usually very consistent, but once in a while, you might get a shocking heatwave or deep freeze that surprises everyone. Low kurtosis means the weather changes gradually every day without sudden shocks.

By looking at kurtosis, we can see if a system is stable with rare big jumps, or steady and predictable without any drama.